Oxygen- and carbon-rich variable red giant populations in the Magellanic Clouds from EROS, OGLE, MACHO, and 2MASS photometry
M. Wisniewski, J.B. Marquette, J.P. Beaulieu, A. Schwarzenberg-Czerny, P. Tisserand, E. Lesquoy
aa r X i v : . [ a s t r o - ph . S R ] A p r Astronomy&Astrophysicsmanuscript no. 14319 c (cid:13)
ESO 2018November 2, 2018
Oxygen- and carbon-rich variable red giant populations in theMagellanic Clouds fromEROS, OGLE, MACHO, and 2MASS photometry.
M. Wi´sniewski , J.B. Marquette , , J.P. Beaulieu , , A. Schwarzenberg-Czerny , , P. Tisserand , , ´E. Lesquoy , , Nicolaus Copernicus Astronomical Centre, Bartycka 18, 00-716 Warsaw, Poland UPMC Universit´e Paris 06, UMR7095, Institut d’Astrophysique de Paris, F-75014, Paris, France, e-mail: (marquett,beaulieu,lesquoy)@iap.fr CNRS, UMR7095, Institut d’Astrophysique de Paris, F-75014, Paris, France Adam Mickiewicz University Observatory, ul. Słoneczna 36, PL 60-286, Pozna´n, Poland, e-mail: [email protected] Research School of Astronomy & Astrophysics, Mount Stromlo Observatory, Cotter Road, Weston ACT 2611, Australia, e-mail: [email protected] CEA, DSM, DAPNIA, Centre d’ ´Etudes de Saclay, 91191 Gif-sur-Yvette Cedex, FranceReceived . . . ; accepted . . .
ABSTRACT
Context.
The carbon-to-oxygen (C / O) ratio of asymptotic giant branch (AGB) stars constitutes an important index of evolutionaryand environment / metallicity factor. Aims.
We develop a method for mass C / O classification of AGBs in photometric surveys without using periods.
Methods.
For this purpose we rely on the slopes in the tracks of individual stars in the colour-magnitude diagram.
Results.
We demonstrate that our method enables the separation of C-rich and O-rich AGB stars with little confusion. For theMagellanic Clouds we demonstrate that this method works for several photometric surveys and filter combinations. As we rely onno period identification, our results are relatively insensitive to the phase coverage, aliasing, and time-sampling problems that plagueperiod analyses. For a subsample of our stars, we verify our C / O classification against published C / O catalogues. With our methodwe are able to produce C / O maps of the entire Magellanic Clouds.
Conclusions.
Our purely photometric method for classification of C- and O-rich AGBs constitutes a method of choice for large,near-infrared photometric surveys. Because our method depends on the slope of colour-magnitude variation but not on magnitudezero point, it remains applicable to objects with unknown distances.
Key words.
Methods: data analysis, Techniques: photometric, Surveys, Stars: oscillations (including pulsations), Stars: AGB andpost-AGB, Magellanic Clouds
1. Introduction
Low and intermediate mass stars evolve through three latestages. After passing the red giant branch (RGB) they reachmaximum luminosity at its tip (TRGB) followed by a luminos-ity drop after the helium flash. Next they grow again and movealong the asymptotic giant branch (AGB). According to theirspectra, the AGB stars split into oxygen-rich stars (O-rich, M-stars, or K-stars) and carbon-rich stars (C-rich, C-stars, or N-stars). The M-stars have more oxygen than carbon in their at-mospheres (C / O < ffi cult and also involves intermediate MS and SC types(Cioni & Habing 2003).Stars entering the AGB phase are rich in oxygen, how-ever, subsequent dredge-up caused by thermal pulsation mayenrich their atmospheres in carbon (Iben & Renzini 1983). Onthe AGB, several thermal pulses (TP-AGB) may occur, resultingin dredging up the matter enriched in carbon nuclei by nuclearfusion. In this way the O-rich stars are converted after at leastseveral pulses into the C-rich ones (Marigo et al. 2008 and ref-erences there). Send o ff print requests to : A. Schwarzenberg-Czerny It is believed that the rate of conversion of O-stars intoC-stars depends on the e ffi ciency of the third dredge-up andthe extent and time variation in the massloss (e.g. Iben 1981;Marigo et al. 1999). Mass loss is expected to be stronger inmetal-rich stars, giving to shorter AGB life and eventually yield-ing a C-star. These thermal pulses result in the luminosity varia-tions with the peak-to-peak amplitude up to a few magnitudes atvisual wavelengths.According to Iben & Renzini (1983), the lower the metallic-ity the less carbon needed to be dredged-up in order to convertan O-star into a C-star, hence the correlation between metallicityand the C / M ratio. For lower metallicity, the AGB evolutionarytracks move to higher temperatures; for very low metallicity apost-horizontal-branch star may become a white dwarf withoutfirst becoming an AGB star. Since O and C stars reveal very dif-ferent spectra, it is relatively easy to spectroscopically identifyC-rich stars even at large distances. The di ff erences in molecu-lar blanketing and dust creation result in an observed sharp di-chotomy in infrared colours of O- and C-rich stars. Thus the O-and C-stars are often identified using narrow filters. The J − K colour of the C-rich stars is > . ff ects influence the luminosity Mariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds function of O- and C-rich AGB stars. The Magellanic Clouds aregood test-beds of theories of the late stages of stellar evolution.They are nearby and yet far enough to ignore the LMC thickness,so that all stars are approximately at the same distance.Late evolutionary stages are often associated with longperiod- (LPV), semi-, and irregular-variability. A wealth ofdata on this variability was collected as a by-product ofthe microlensing surveys. All yielded catalogues of numer-ous variable stars. In these data the period-luminosity rela-tions of the LPV’s on the AGB are well documented for boththe Large and Small Magellanic Clouds (Wood et al. 1999;Wood 2000; Cioni et al. 2001, 2003; Noda et al. 2002, 2004;Lebzelter & Hinkle 2002; Ita et al. 2004a,b; Kiss & Bedding2003, 2004; Soszynski et al. 2004a,b, 2005; Groenewegen 2004;Fraser et al. 2005; Raimondo et al. 2005).The period-luminosity diagram for red variables at advancedevolutionary stages reveals six sequences for di ff erent classesof objects (Ita et al. 2004b). Miras and some low-amplitudesemiregulars pulsating in the fundamental mode form the se-quence C. Other semiregular stars pulsating in the second andthird overtone modes occupy sequences A, B, and C, and theRGB eclipsing binaries form their own sequence E. The origin ofthe sequence D corresponding to long-secondary periods (LSP)remains ambiguous. Wood et al. (2004) considered a number ofpossible explanations of LSP (radial and non-radial pulsations,rotations, orbiting companions, chromospheric activity, orbitingdust clouds), but none fit the observations satisfactorily.Soszynski et al. (2004a) combined the OGLE-II and OGLE-III data and found the multiperiodicity of the red giants to bevariable with a small amplitude. They exhibited two modesclosely spaced in their power spectrum. This is likely to indi-cate non-radial oscillations. They also show that members of theshort-period P–L sequences below the TRGB constitute a mix-ture of the RGB and AGB variables. Recently, Soszynski et al.(2004a, 2005); Soszy´nski (2007), and Derekas et al. (2006) havedemonstrated that the sequence E overlapped with the sequenceD, which may be evidence for a binary origin of the sequence D.There are di ff erences between the O-rich and C-rich LPVs,too. Cioni et al. (2003) note that C-stars have a larger amplitudethan O-stars. Ita et al. (2004a) confirm that O- and C-rich Mirasfollow di ff erent period vs. ( J − K ) colour relations (Feast et al.1989). The I-band amplitude of C-rich Miras tends to grow withthe redder mean ( J − K ) colour, while the amplitude of O-richMiras is colour independent (Matsunaga et al. 2005).The evidence has provided new and significant con-straints for theoretical pulsation models. Models and obser-vations are compared in three ways: using stellar isochrones(e.g. Bressan et al. 1996; Bruzual & Charlot 2003; Mouhcine2002; Marigo et al. 2003; Groenewegen & de Jong 1993),stellar tracks (Groenewegen & de Jong 1993; Marigo et al.1999; Mouhcine & Lanc¸on 2002; Lanc¸on & Mouhcine 2002;Mouhcine & Lanc¸on 2003), and the fuel consumption theoremby Renzini & Buzzoni (1986) and Maraston (1998, 2005).The synthetic characteristics of AGB stars are derived eitherfrom complete evolution tracks, semi-empirical fits to the coremass-luminosity relation, or from the core mass-interpulse pe-riod relation and the mass-loss rate as a function of stellar pa-rameters. The examples of such calculations are provided byGroenewegen & de Jong (1993) and Izzard et al. (2004).Recent attempts have been made to include the TP-AGBphase in evolutionary population synthesis models. Both im-provements in the low-temperature opacities and peculiaritiesof the actual surface chemical composition have such profoundconsequences that the whole AGB evolutionary scenario be- came significantly a ff ected (Marigo et al. 2008). Use of themolecular opacities reflecting the actual chemical compositionleads to a significant decrease in T e f f as soon as C / O > J − K ) colour-magnitude diagram of C stars.The mass loss is driven by pulsation in a complicated way.The pulsation pushes a fraction of the atmosphere above thephotosphere, creating a cool and dense environment where dustgrains form and grow e ffi ciently. The radiation pressure on thedust combined with the momentum carried in the shock wavesdrives the mass loss (Wood 1979; Bowen & Willson 1991;Hoefner et al. 1996, e.g.)Lebzelter & Wood (2005) compared the observations ofLPV in 47 Tuc with the models. On one hand, they find thatthe models without mass loss fail to reproduce the observed pe-riods of the small amplitude pulsators. On the other, the K − log P sequence of the large amplitude variables, such as the Miras, isinconsistent with the mass-oss models and consistent with the nomass-loss models. Only models involving the non-linear funda-mental mode yield periods consistent with the Miras in 47 Tuc(Olivier & Wood 2005).The past decade has brought results of extensive pho-tometric surveys – OGLE (Paczynski et al. 1994), OGLE II(Udalski et al. 1997), EROS (Aubourg et al. 1995), MACHO(Alcock et al. 1997), and MOA (Bond et al. 2001) – coveringseveral optical and infrared bands, sometimes simultaneously.They have provided a wealth of observations of red variablestars, thus enabling the study of their population properties. Inparticular, use of infrared colours and / or pulsation periods haveenabled the classification of C- and O-rich stars. We discussedabove the relevant observational and theoretical results.In the present paper, we attempt to analyze the photomet-ric properties of red variables in the visual region without re-course to their periods. Our analysis should be complementaryto any traditional methods while su ff ering less, if at all, fromaliasing and seasonal interference. We employ correlation slopesof colour and magnitude variability introduced by Wood et al.(2004). In this paper the slope a R of the correlation of R magni-tude and V − R colour variations revealed no relation with anyother property of red variables. We employ a di ff erent filter com-bination in our attempt of photometric classification of C and O-rich red variable stars. Our results should not depend much onthe number of pulsation cycles covered by a given survey. Ourpractical requirement that data span at least one pulsation cycle,is met in most large surveys.In Sect. 2 we describe data employed in the present study.Our calculation methods are described in Sect. 3. In Sect. 4 wepropose new methods of selection O- and C-rich stars. Due tolarge di ff erences in filters and time span, we present our resultsfor each survey separately. We give an estimate of the C / O ratiofor variable stars in the Magellanic Clouds. In Sect. 5 we employa simple model to demonstrate how observed e ff ects may arise.Possible peculiar variables are discussed in Sect. 6. We concludein Sect. 7.
2. The data
Our paper is based primarily on the EROS-2 photometric surveyof the Magellanic Clouds cross-referenced with the 2MASS in-frared magnitudes (Sect. 2.1). We explicitly indicate when theseare supplemented by the OGLE and MACHO photometry andfour catalogues of C-and O-rich stars (Sect. 2.2 – 2.4). ariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds 3
The Exp´erience de Recherche d’Objets Sombres (EROS-2)project employed extensive photometry obtained with the 1-meter MARLY telescope at La Silla Observatory, Chile, tosearch for the baryonic dark matter of the Galactic haloby means of the gravitational microlensing (Afonso et al.2003; Lasserre et al. 2000; Palanque-Delabrouille et al. 1998;Tisserand et al. 2007). The observations were performed be-tween July 1996 and February 2003 through a dichroic plate-splitting light into two wide field cameras covering 0 . × . o inright ascension and declination each, yielding two broad pass-bands. The so-called blue channel (420 −
720 nm, hereafter B E band) overlapped the standard V and R standard bands, whilethe red one (620 −
920 nm, hereafter R E band) roughly matchedthe standard I filter. Each camera constituted a mosaic of eight2 k × k CCDs with a pixel size on the sky of (0 . .Ten fields covered the SMC and 88 fields covered the LMC.The photometry from individual images was combined into lightcurves using the Peida package developed specifically for theEROS experiment (Ansari 1996). The estimated accuracy of thisphotometry is discussed by Derue et al. (2002). For uniformity,the SMC data were analysed again with the more recent versionof Peida.The RGB and AGB variable stars were selected from theSMC and LMC lists of EROS variables using their location inthe colour-magnitude diagram. In this way we selected 28914stars in LMC and 5930 in SMC. They constitute our sample usedin further analysis. The Optical Gravitational Lensing Experiment (OGLE-II) datawere collected with the 1.3 m Warsaw Telescope at theLas Campanas Observatory, Chile, operated by the CarnegieInstitution of Washington. The I -band data span about 3000days: from January 1997 to April 2005. The V -band measure-ments were obtained from 1997 to 2001 (Zebrun et al. 2001), sothey span a shorter time baseline. Up to 70 V -band points perstar are available. In the I -band, 500 to 900 measurements wereavailable, depending on the field (Soszynski et al. 2005). In thepresent work we use data on 3586 LPV from LMC publishedby Soszynski et al. (2005), downloaded from the OGLE home-page .We cross-identified EROS and OGLE objects within a 1 . The MAssive Compact Halo Objects (MACHO) project(Alcock et al. 1997) comprises eight years of observations ofthe Large and Small Magellanic Clouds and of the GalacticBulge. For the present purposes we selected LMC stars from theMACHO catalogue of variable stars (Alcock et al. 2003). Usingthe MACHO interface, we downloaded 2868 individual lightcurves of the stars classified as the red giant variables (classifiedas Wood A, B, C, and D sequences). http: // sirius.astrouw.edu.pl / ∼ ogle / http: // / The Two Micron All Sky Survey (2MASS) employed two 1.3-m robotic telescopes, one at Mt. Hopkins, Arizona, and one atCTIO, Chile. Each telescope was equipped with a three-channelcamera, capable of observing the sky simultaneously at J (1.25microns), H (1.65 microns), and K s (2.17 microns). The south-ern facility began collecting Survey data in March 1998 and con-ducted its final scan in February 2001.We extracted 2MASS data for each of the EROS fields sep-arately. Then cross-identification was done separately for eachfield. During the cross-identification of EROS and 2MASS, weemployed a 3” search radius. We selected only stars with pho-tometry available in all three bands J , H , and K s . AGB stars areamong the brightest stars of the LMC. If an area of the order of16 square degrees contains 25000 AGB stars, their average sep-aration is 1.5 minutes of arc, so the probability of blending twoof them within the search radius is (1 . ∗ / − = . K <
12 for LMC and K < . a V versus K diagrams. One possible problem is mixing faintAGBs with RGBs, causing pollution of RGBs with AGBs but nototherwise [i.e. faint AGB remain clean, if possibly incomplete].Kiss & Bedding (2004) consider the same problem in more de-tail for stars from OGLE and 2MASS and conclude that con-tamination is insignificant, possibly no more than 0.3%, for theirsearch radius of 1”, corresponding to less than 3% contaminationfor our radius of 3”. Since there were selected MACHO objectsthan for EROS, we cross-identified MACHO and 2MASS with-out subdivision into fields and with the same 3” radius. Againwe only selected stars with photometry in all three bands J , H ,and K s . We selected 1707 C-rich stars from the SMC identifiedby Rebeirot et al. (1993) in the low-resolution spectroscopicsurvey employing the ESO 3.6 m telescope and 1185stars identified in the Siding Spring Observatory survey byMorgan & Hatzidimitriou (1995).A catalogue of 7760 C-rich stars in the LMC was presentedby Kontizas et al. (2001). These stars were identified during asystematic survey of the objective-prism plates taken with theUK 1.2 m Schmidt Telescope. To these we added the list of C-rich stars from Groenewegen (2004).Soszynski et al. (2005) demonstrate a new method of dis-tinguishing between O-rich and C-rich Miras, SRVs and starswith long secondary periods, relying on their V and I -band pho-tometry and periods. The list of stars selected from the LMC inthis way was downloaded from the OGLE homepage. All C-richstars from these catalogues were cross-identified with the EROSand MACHO stars within a 3” radius. http: // / / Mariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds
3. Data pre-processing
The analysis outlined in this paper was performed separately forEROS LMC and SMC, OGLE LMC and MACHO LMC data.We used data from all surveys to study a path in the colour-magnitude diagram traversed by each variable star. We investi-gated correlation of the average slope of the path with the chem-ical composition of the objects. The results of this analysis aresummarised in diagrams described in the Sect. 4.The EROS survey produced simultaneous light curves in twospectral bands. By applying time filters to each band light curvewe obtained a smooth, low-pass filtered light curve and its com-plementary high-pass light curve. The sum of the two reproducesthe original light curve. In this way for each spectral band weobtained 3 light curves: raw, low-, and high-pass, six in total. Infurther analysis we study correlations of stellar properties withthe properties derived from these light curves.
Both EROS and MACHO obtained simultaneous expositions intwo bands termed “red” ( R E and r , respectively) and “blue” ( V E and v , respectively) for nearly all observations. We simply ig-nored observations made in just one filter.Following Tisserand et al. (2007), we converted the raw pho-tometry into the standard Kron-Cousins system using the follow-ing relations: V EROS = . V E − . R E (1) I EROS = R E . (2)The MACHO data from the web database are available inthe raw instrumental system. Following Alcock et al. (1997), weconverted the raw photometry into the standard Kron-Cousinssystem using the following relations: V MACHO = v + . − . v − r ) (3) R MACHO = r + . − . v − r ) (4)where v and r are instrumental magnitudes and V MACHO and R MACHO are in the Kron-Cousins standard system. These cali-bration formulae are estimated to have an overall absolute ac-curacy of ± .
10 mag in V MACHO or R MACHO and ± .
04 mag in( V − R ) MACHO (Alard et al. 2001).The OGLE survey employs one camera, so observations indi ff erent filters are not simultaneous. Observations in V filterwere obtained much less frequently than in I . For each V ob-servation, we searched the nearest I observations. If two I pointsbefore and after a V observation separated by no more than 2days, we performed a linear interpolation at the time of V obser-vation. For just one I point nearby, no more than one day fromthe V observation, we assume they were measured nearly simul-taneously. In this way for most V observations we found its cor-responding I magnitudes. Other V observations were ignored.Because we only analyse stars with long periods, this procedureproved reliable for our purposes. Through the whole paper except for Sect. 6, we used the rawlight curves. Light curves for Sect. 6 were filtered in the timedomain. The low-pass curve was obtained from the raw one bymeans of the “moving median”. The purpose of time filtering isto separate short period pulsations in some stars from the LSP.Since our procedure does not depend on actual detection of these -0.4-0.2 0 0.2 0.4-1 -0.5 0 0.5 1 ∆ V -I ∆ V -0.4-0.2 0 0.2 0.4-1 -0.5 0 0.5 1 ∆ V -I ∆ V Fig. 2.
Sample plot of raw colour and magnitude variations forthe same 2 stars as in Fig. 1. We also plot the regression lines.Their inclination parameter is a V , discussed in the text.periods, we applied it to all EROS red variables. We selecteda window of width w centred on a given point and replaced itsvalue with the window median value. In practice we filtered eachlight curve twice consecutively using windows of width w and w dependent on average K s luminosity: w = ( K − D ) / ( − . (5) w = ( K − D + / ( − . (6)where the D magnitude is equal to 19.4 for the LMC and to 21.1for the SMC. These windows were selected to have intermediatelength between the short period and LSP (see Sect. 6 for discus-sion of these periods). As both periods depend on mean stellarbrightness K , so do our window widths. The slope of − . P − L ) diagram(Ita et al. 2004b; Soszynski et al. 2004a). As this area is virtu-ally devoid of stars, its exact value is of no consequence for thecurrent considerations.We found that a light curve smoothed with two movingmedians reveal LSP more clearly than when smoothed onlyonce. Any short-period variations are filtered out. The high passcurve was obtained by subtracting the low pass one from theraw data. Only short time variations are left in the high-passlight curve. Sample light curves are plotted in Fig. 1. A simi-lar procedure was employed by Wood et al. (2004) except thatwe did not use the short period as the parameter determining fil-ter window to avoid confusion for multi-periodic / irregular redgiants (Soszynski et al. 2004a). For EROS and MACHO colours( V − I ) EROS , ( V − R ) MACHO were calculated for each time point.Subsequently we filtered colours similarly to how magnitudesare filtered. In this way we got the colour variation for raw data,LSP, and short time scale variations separately. For OGLE thenumber of V observations was too small to filter. In further analyses we considered variations in colour againstmagnitude, for all possible combinations of light curves (raw,long-, and short-time scale colours against raw, long- and short-time scale V and I magnitudes). Sample plots are presented inFig. 2. Next we fitted by the least squares the regression lines,( V − I ) = a I I + b I (7)( V − I ) = a V V + b V (8)where a V and a I denote the slope of the corresponding colour- magnitude relation. This kind of linear equation was fitted forEROS, OGLE and MACHO data.To verify the quality of our slope parameter, we calculatedthe correlation coe ffi cient ρ and the statistic t in the following ariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds 5 -0.6-0.4-0.2 0 0.2 0.4 0.6 500 1000 1500 2000 V r a w time -0.6-0.4-0.2 0 0.2 0.4 0.6 500 1000 1500 2000 V l ong time -0.6-0.4-0.2 0 0.2 0.4 0.6 500 1000 1500 2000 V s ho r t time-0.6-0.4-0.2 0 0.2 0.4 0.6 500 1000 1500 2000 V r a w time -0.6-0.4-0.2 0 0.2 0.4 0.6 500 1000 1500 2000 V l ong time -0.6-0.4-0.2 0 0.2 0.4 0.6 500 1000 1500 2000 V s ho r t time Fig. 1.
Sample EROS light curves for two stars with spectral types assigned by Cioni et al. (2001): DCMC J052618.12-694100.0of type C (top row) and DCMC J052446.91-694949.9 of type M (bottom row). The left, middle, and right panels present the raw,low-pass, and high-pass light curves, respectively. For details of filtering see Sect. 3.2way: ρ = Cov { V , V − I } σ V σ V − I (9) t = ρ p − ρ √ n − Cov { V , V − I } = n n X i ( V − V )[ V − I − ( V − I )] . (11)Results are shown in Fig 3. For the null hypothesis H assumingno correlation, i.e. ρ =
0, a t statistic obeys the Student distribu-tion with n − n is number of pointsper star (Fisz 1963). For a probability of 0.995, t is equal to 2.6.For most stars the correlation coe ffi cient is greater than 0.5, and t is as significant as 15 or more. The amplitude of the luminosity variation was calculated fromthe distance of the maximum and minimum in the correspond-ing, possibly filtered light curve. We derived the amplitude ofthe colour variation as the distance between points on these linescorresponding to extreme magnitudes. In this way we dimin-ished the influence of individual colour errors on the colour am-plitude. These amplitudes were calculated for each filter, and raw, long-, and short time-scale data.
4. Photometric chemical classification of redvariable stars
Wood et al. (2004) have introduced the variability slope parame-ter a R . They note it has no obvious relation to any other propertyof red variable stars. Noticing that red giants have greater am-plitude in the blue filter results in better accuracy for the slopeestimates. We adopted the a V slope parameter as a better substi-tute. In the left panels of fig. 4 we plot the slope a V of the colour - blue magnitude relation against amplitude, for all EROS redvariable stars in the LMC and SMC. For completness we alsoplot a V against the near infrared magnitude and colour in themiddle and right panels. In the rest of the present section, we in-vestigate our slope parameter a V as a tool for the chemical and / orevolutionary status classification of red variable stars. We defer adiscussion of the classification corresponding to the middle andright panels until Sects. 4.3 and 4.4. Anticipating our result, weadopted in Fig. 4 di ff erent colour coding for O-rich RGB stars,O-rich, and C-rich AGB stars as green(light grey), blue(black),and red(dark grey) dots, respectively. The colour-coded selec-tion, for all diagrams, comes from the third method presented inthe right panels.The left panels in Fig 4 display plots of the slope a V againstthe colour amplitude amp VI for EROS LMC and SMC data, re-spectively. Note the conspicious two-modal distribution of aVsuggesting separate clustering of C- and O-rich AGB stars. Inthese plots there are two distinct branches corresponding tosteep and shallow slopes, i.e. for large and small a V . For bothbranches, the slope initially grows and then, for amplitudes over0.3, saturates at the constant values of 0.65 and 0.3. These twogroups can be separated by the curve with the equation a V = .
52 tanh( amp VI / . . (12)The same border holds for both EROS LMC and SMC data. Inthe following sections we demonstrate by cross-checking in thecatalogues that the stars above and below the curve are respec-tively O- and C-rich. Thus our Eq. (12) constitutes the new clas-sification criterion for C- and O-rich stars. Its importance andnovelty stem from using the visual photometry alone with norecourse to periods. Our criterion does work for an incompletephase coverage and even for data spanning as small an intervalas a typical Mira period. Moreover, at this point there are no ob-stacles to test the usefulness of our new method for the semi- andirregular red variables. Problems in using a I for low-amplitudevariables are illustrated in Fig. 5. The two clusters merge for lowamplitudes. In this way we confirm that the slope a V is indeed Mariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds a V amp VI LMC 0 0.2 0.4 0.6 0.8 1 9 10 11 12 13 14 a V K LMC 0 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 a V J-K LMC 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 a V amp VI SMC 0 0.2 0.4 0.6 0.8 1 9 10 11 12 13 14 a V K SMC 0 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 a V J-K SMC
Fig. 4.
Plots depicting three methods of distinguishing O- and C-rich variable stars (from left to right): slope-colour amplitude a V ( amp VI ), slope- K magnitude a V ( K ) and slope- J − K colour a V ( J − K ), for EROS LMC (top) and SMC (bottom) data. Verticallines indicate adopted TRGB dividing RGB and AGB stars. See text for a detailed description of the methods and parameters of theboundaries. Black, dark grey, and light grey dots (blue, red, and green in electronic edition) respectively mark O- and C-rich AGBstars and O-rich RGB ones, classified using K magnitudes for AGB / RGB and leftmost panels for O / C content. a V amp VI LMC 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 a I amp VI LMC
Fig. 5.
Comparision of a V plot in Fig. 4 with that for a I .much more suitable for classification purposes than our a I and a R used by Wood et al. (2004).In Sects. 4.2, and 4.6, we verify our classification against ex-isting catalogues, while in Sects. 4.3 – 4.5 we discuss alternativephotometric systems. Of the 50 stars assigned by Cioni et al. (2001) spectral types C,M, and S, 30 lie in our fields and have entries in 2MASS. In Fig.6 we plot them in the same way as in Fig 4. Spectroscopic andphotometric grouping is consistent in general and that in partic-ular the S-stars lie on the border between C and M stars, as ex-pected. Clear separation of C and M stars in the left panels con-stitutes the most reliable test of our method. More extensive testsfollow from cross-identifying of the stars from EROS, OGLE,and MACHO with the spectroscopic catalogues of C-rich starsby Kontizas et al. (2001) and Groenewegen (2004) for the LMCand by Rebeirot et al. (1993) and Morgan & Hatzidimitriou (1995) for the SMC (Sect. 2.5). For this purpose the optical ( V , I ) magnitudes were obtained from EROS, OGLE, and MACHOphotometry, while infrared ( J , K ) magnitudes were obtained bycross-reference with 2MASS (Sects. 3.1, 2.2, 2.3, and 2.4). InFig. 7 we plot all identified C-rich stars in tha same fashion asin Fig. 4. The border lines in Fig. 7 are plotted for correspon-dence with Fig. 4. All previous succesful photometric criteriawere based on the infrared colours (c.f. middle and right panels,e.g. Soszy˜nski et al. (2009)).Some confusion in the distribution may be caused by pres-ence of the intermediate S type stars with the number of O-atomsequal to that of C-atoms. This confusion arises from the di ffi -culty of classifying the S stars using the low-resolution spectraobtained for the catalogues employed in this section. Infrared colour and luminosity may be employed to addition-ally split red stars according to their evolutionary status. In the ariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds 7 a V amp VI LMC 0 0.2 0.4 0.6 0.8 1 9 10 11 12 13 14 a V K LMC 0 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 a V J-K LMC
Fig. 6.
Similar plots as in Fig. 4 for C-rich, O-rich, and intermediate stars of Cioni et al. (2001), of respective spectral types C(triangles), M (circles), and S (squares). a V amp VI LMC 0 0.2 0.4 0.6 0.8 1 9 10 11 12 13 14 a V K LMC 0 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 a V J-K LMC 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 a V amp VI SMC 0 0.2 0.4 0.6 0.8 1 9 10 11 12 13 14 a V K SMC 0 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 a V J-K SMC
Fig. 7.
C-rich stars in LMC (upper panels) from Kontizas et al. (2001)and Groenewegen (2004) and in SMC (lower panels) fromRebeirot et al. (1993) and Morgan & Hatzidimitriou (1995). Colour-slope parameter a V in function of: amplitude of colour change amp VI (left panels); K J − K colour (right panels).middle panels in Fig. 4 we plot slope a V against K luminos-ity for EROS LMC and SMC, respectively. The separation ofthe C- and O-star sequences is as clearly visible as before, yetthe O-sequence terminates abruptly near the K magnitude ofthe TRGB of 12 and 12.7 for the LMC and SMC, respectively(Cioni et al. 2000c). The di ff erence in magnitudes correspondsto the di ff erence in distance moduli of the LMC and SMC. Thehorizontal line at a V = a V grows with K magnitude. As soonas they reach the AGB, the slope saturates. The skew separationlines plotted in the figures correspond to the equations a V < − . K + .
31 for K > . a V < .
52 for K . a V < − . K + .
51 for K > . a V < .
52 for K . K luminosity of the AGB and RGB stars overlaps to someextent. A fraction of the AGB stars exists with luminosity be-low that of the TRGB. Since the RGB and O-rich AGB starshave similar slopes, the RGB region is tainted with some O-richAGB stars. In the above, we only employ K magnitudes for mor-phological purposes to separate stars on the colour diagrams. Forstars with dust shells, the K magnitude fails as a bolometric lumi-nosity indicator; however, in the present paper we concentrate onoptical photometry, and for the detailed discussion of IR proper-ties the reader is referred to the original papers. J − K colour diagram. In the infrared, the C-rich stars appear systematically redder ( J − K > .
4) than O-rich stars (Frogel et al. 1990; Costa & Frogel1996; Cioni et al. 2000a; Soszynski et al. 2005); however, in K vs. J − K diagrams (Fig. 8) there is some overlap between the Cand O regions. The e ffi cient way to separate the C and O stars isto combine the slope a V with the J − K colour. In the right panelsof Fig. 4 we plot slope a V against J − K . Now separate clusteringof C- and O-rich stars becomes more obvious. Based on this wepropose the following criterion for C-rich stars: a V < / K + /
15 and J − K > . . (17) Mariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds ρ a V LMC 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ρ a V SMC
Fig. 3.
Plot of the colour-magnitude correlation coe ffi cientagainst the slope of magnitude-colour relation, for EROS LMCand SMC data. The correlation coe ffi cient serves as a measure ofquality of the slope a v . The horizontal lines correspond to prob-ability 0.995 of the null hypothesis H , i.e. points lying abovecorrespond to statistically significant correlation.This criterion corresponds to the colour coding of stars in allpanels in Fig. 4. Oxygen stars were separated from RGB andAGB using TRGB.The Z-like shape of the distribution of stars in the a V - ( J − K )panels in Fig. 4 represent the evolutionary sequence from O-richRGB (top left) through O-rich AGB (right) down to C-rich AGBobjects. For O-rich RGB stars, amplitudes tend to be low (leftpanels in Fig. 4) and slope parameter a V is poorly constrained.For higher luminosity O stars beyond TRGB, the slopes arebetter determined and stars concentrate around a V = .
65 and J − K = .
2. When TP-AGB begins and C-rich matter showson the surface, the star migrates towards the inclined border linewhere there are stars with intermediate MS, S, and SC types.Eventually after crossing the border, it lands in the C-rich AGBstar cluster. There is no appreciable di ff erence between diagramsfor the LMC and SMC. Using a V , K , and J − K we cannot onlyclassify stars but also we could roughly determine its evolution-ary stage. No such direct evolutionary interpretation was avail-able for our slope parameter diagrams; however, this was madeby resorting to cross identification of stars in the infrared andoptical catalogues, and looking for which slope diagram con-centrations correspond to the concentrations in the IR diagram. K J-K LMC 9 10 11 12 13 14 0.5 1 1.5 2 2.5 K J-K SMC
Fig. 8.
K - J-K diagram for LMC and SMC red variables.
The Wesenheit index is a reddening-free parameter defined bya linear combination of stellar magnitudes. For EROS bandsit could be calculated from the following equation (e.g. Tanvir(1997) and references there): Wi EROS = I EROS − . V EROS − I EROS ) (18)where I EROS and V EROS are light curve average magnitudes(Sect. 3.1). For EROS, observations in both filters are simulta-neous so time sampling yields no big uncertainty in colours.Plots of Wi EROS against the K magnitude for EROS LMCand SMC are presented in Fig. 9. Separation of C- and O-starsbecomes particularly clear for the LMC. The location of threegroups of stars with respect to the TRGB is visible in theseplots. Similar diagrams for the Wesenheit index were alreadypresented by Noda et al. (2002) and Soszy˜nski et al. (2009), butour filter bands and fields are rather di ff erent. In particular theaccuracy of the estimation of the Wesenheit index is sensitive tothe quality of the two-band coverage. For EROS the advantagestems from the simultaneous observation in two bands.As the Wesenheit index is well correlated with K magnitude,it is in principle possible to implement the method of Sect. 4.3by relying purely on EROS visual observations. In particular theWesenheit index would be helpful to separate the RGB and AGBstars; however, such a classification would be less precise thanthan the one based on K luminosity. The gap on TRGB, clearlyvisible in K distribution, is hard to find in Wi . We can also sep-arate RGB from AGB stars using the I-band. The TRGB appear ariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds 9 W i E R O S K LMC 11 12 13 14 15 16 9 10 11 12 13 14 W i E R O S K SMC
Fig. 9.
EROS Wesenheit index vs. K magnitude, for LMC andSMC red variables. Wesenheit index is derived from EROS Rand B magnitudes.at I = .
54 in the LMC and I = .
95 in the SMC (Cioni et al.2000b).
The bands employed by the EROS survey were non-standard.In this respect it is desirable to verify our results with OGLEobservations obtained in the standard I and V bands. For theOGLE light curves, we performed the calculations similar tothose for EROS. In this way we obtained values of the corre-sponding slope a V . The results for OGLE are presented in Fig.10. We only plot LPV selected by Soszynski et al. (2005), whoreject low-amplitude variables. Thus the number of stars withlow colour amplitude and low K luminosity is lower than forEROS LMC.Nevertheless, features revealed in Fig. 4 are present in Fig.10. It is remarkable that, despite the small number of V obser-vations and the interpolation of I magnitudes, separation of starsinto respective classes is clear.Soszynski et al. (2005) suggest that this sample should onlycontain the LPV AGB stars. We found that below the TRGBtheir stars follow the relation corresponding to the RGB stars.This may indicate that these stars belong to the AGB or at leastthat they follow the same relation as the RGB. These authorsintroduced the Period-Wesenheit index plots for a new methodto di ff erentiate between the O- and C-rich stars. Our method in- a V amp VR LMC 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 9 10 11 12 13 14 a V K LMC
Fig. 11.
Slope a V against V − R amplitude amp VR (top) andagainst 2MASS K magnitude, for MACHO LPV V and R pho-tometry of the LMC. The C-rich stars are marked with circles.troduced in Sect. 4 is complementary as we use no informationon periods. In this way our method is less demanding on timecoverage of the light curves. Nevertheless, the two methods ofselection of O- and C-rich stars are fairly consistent. The same procedure as for EROS was repeated for the MACHOdata. MACHO uses non-standard filters fairly close to the stan-dard V and R rather than V and I . In this way MACHO bandsdi ff er markedly from those of EROS and OGLE. This di ff erencestrongly a ff ects our results for MACHO. The plots of the slope a V against either the colour amplitude for MACHO bands or the2MASS K mag reveal no clear separation of the O- and C-richstars in Fig. 11. This result seems consistent with the failure ofthe Wood et al. (2004) classification of the O- and C-rich starsbased on similar filters. Thus our method only works for suit-able photometric bands and is useless for MACHO photometry. In Table 1 we compared the three new methods described in Sect.4.1, 4.3 and 4.4 with the well known method K ( J − K ) that uses J − K > . a V amp VI LMC 0 0.2 0.4 0.6 0.8 1 9 10 11 12 13 14 a V K LMC 0 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 a V K LMC
Fig. 10.
Separation of C-rich, O-rich AGB, and red variables below the TRGB for LMC from OGLE LPV I and V photometry(Soszynski et al. 2005). The colour slope parameter a V vs. the amplitude of colour change (left panel). The colour slope parameter a V vs. K J − K colour (right panel). Table 1.
The C / O ratio for the MC’s from variable stars
Method K ( J − K ) a V ( amp VI ) a V ( K ) a V ( J − K )LMC 0.63 0.69 0.69 0.72SMC 0.46 0.89 0.98 0.81 method. The K ( J − K ) method yields the conclusion that the C / Oratio is much lower for the SMC than for the LMC. The a V ( J − K )method yields the opposite result: the C / O ratio is greater in theSMC than in the LMC. Right panels of Fig. 4 shows that manyC-rich stars lie between 1.15 and 1.4 on the J − K axis, especiallyfor the LMC and a V ( J − K ) can separate stars without problem inthis range of J − K . Di ff erent distributions of C-rich stars in theMagellanic Clouds probably depend on metallicity. Stars in theSMC are bluer than in the LMC for a similar stage of evolution.Table 1 also contains results for a V ( amp VI ) and a V ( K ) meth-ods. To compare a V ( amp VI ) with other methods, we divided O-rich stars to RGB and AGB stars using TRGB. Both methods area ff ected by overlapping O- and C-rich regions but still we foundmore C-rich stars than with the the K ( J − K ) method.From our samples of O- and C-rich AGB stars from the a V ( J − K ) method, we calculated the C / O ratio in all cells be-longing to a grid of 100’ × ×
45’ over the face of the SMC. Figure 12 shows theratios after boxcar average smoothing. A large hole in the centralpart of the SMC results from the lack of data in that sector. Weretreive the same trends as described by Cioni & Habing (2003)in their Figs. 3 & 4: in the LMC the higher values of the C / Oratio are located in the outer regions, while the structure in theSMC is clumpier.
5. Clues to the underlying scenarios
Detailed modelling of the observed e ff ect is beyond the scope ofthe present paper. As we pointed out above, modelling the lateevolutionary stages is di ffi cult and constitutes a whole branchof the theory. Worse, reconstruction of the synthetic spectraof C-rich AGB stars proved di ffi cult and strongly relies onprogress in the low-temperature opacities (Marigo et al. 2008).Simulation of the pulsations of the AGB stars is still more com-plex. The stellar atmosphere during pulses does not move uni-formly up or down (Ireland et al. 2004b,a). Thus the non-linearpulsation model of a red giant is required to fit observations(Lebzelter & Wood 2005; Olivier & Wood 2005; Wood 2006).However, it is possible that the e ff ect demonstrated in Sect.4 does not depend strongly on the details of the underlyingphysics. To demonstrate that we resorted to a crude and pos- d ec . [ d e g ] d ec . [ d e g ] Fig. 12.
Maps of the C / O ratio in the LMC (upper panel) andin the SMC (lower panel) obtained from EROS data using the a V ( J − K ) method described in Sect. 4.4.sibly non-physical model assuming that for all AGB stars dur-ing pulses d log L / d log T e f f = const and that the amplitude ofvariation in L and T e f f remains the same for all stars. Thus anyobserved di ff erences between stars would follow from a di ff er-ent response by their envelope to the same modulation. Next, weassume that the response of the upper envelope is quasi-staticand may be determined by interpolation between di ff erent stat-ics, i.e. non-pulsating, evolutionary models from di ff erent tracksbut with the suitable L and T e f f . This could be far from reality. ariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds 11 a V amp VI model 0.5 0.55 0.6 0.65 0.7 -10-9-8-7-6-5-4 a V K model 0.5 0.55 0.6 0.65 0.7 0.5 1 1.5 2 2.5 a V J-K model
Fig. 13.
Same as in Fig. 4 for the model slope parameter a V calculated for real LMC stars using Marigo et al. (2003) model sequences(see text for details). Our crude model yields a clear separation of O-rich RGB, O-rich AGB, and C-rich AGB stars.We employed the tracks calculated by Girardi & Marigo(2007) and available for download to interpolate propertiesof individual stars at their extreme luminosities. we take lu-minosity L , e ff ective temperature T e f f , absolute bolometricmagnitude M bol , absolute magnitudes in Johnson-Cousin-Glass U BVRI JHGK pass-bands, and surface carbon-to-oxygen num-ber ratio C / O listed for the tracks. We interpolated these valuesto find how luminosities in filters vary with L and T e f f duringpulsation. In each track we identified the location of the RGBstars during TRGB and AGB phases of evolution. Next we per-turbed their L and T e f f to simulate the pulsation extreme phases.Using the corresponding filter magnitudes, we calculated slopesand amplitudes and plotted them in a similar way as for Fig. 4.By trial and error we found that a reasonable match with Fig.4 is obtained for ∆ log T e f f = . ∆ log L = . d log L / d log T e f f = . K luminosity and slope-colour J − K diagrams.As our model is entirely artificial, we refrain from strongconclusions. However, this result should encourage theoreticiansto reproduce our e ff ect using fully realistic calculations (e.g.Marigo et al. 2008), and to use it to restrict the pulsation sce-nario.
6. Special properties of red variables.
So far, our analysis has concerned the red variable stars with amodest amplitude ( amp V < In Fig. 14 we plot the slope- against colour amplitude for thewhole range of amplitudes. This figure, which based on the rawdata, corresponds exactly to the left column in Fig. 4, except forthe extended amplitude scale. To illustrate here and in the nextfigure the relation of colour and luminosity amplitudes, amp VI and V , stars to the right of the line of inclination 0.6 passingthrough the origin are marked with di ff erent symbols. It appearsthat the pattern of the two populations of stars with small and http: // pleiadi.aopd.inaf.it a V amp VI LMC 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 a V amp VI SMC
Fig. 14.
Colour-slope parameter in function of amplitude ofcolour change for EROS LMC and SMC data. Crosses marklarge-amplitude variables.large slopes discussed in Sect. 4 does extend to the large ampli-tudes, too. On a related plot of Wesenheit index vs. K luminosity,the large-amplitude C-rich stars appear redder, while the O-richones are bluer then the corresponding stars of small amplitude.We found no other peculiarities for the large-amplitude stars. Up to now we have analysed the raw data. However, many RGBvariables reveal combinations of two periodic variations: a shortone, presumably a radial pulsation, and a LSP. The correspond- a m p V - l ong amp V-short
LMC 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 a m p V - l ong amp V-short
SMC
Fig. 15.
Correlation between amplitudes of LSP and of shorterperiod variation for EROS LMC and SMC data. Crosses marklarge-amplitude variables.ing periods form sequences B / B ′ and D in the period- luminositydiagram (P-L). The nature of the LSP in RGB stars is still a mys-tery for interpretation (Soszy´nski (2007); Nicholls et al. (2009)and references therein). The D sequence periods are roughly tentimes longer than the B ones and correspond to no known ra-dial pulsation mode. The B sequence may correspond to a low-number overtone radial mode. LSP is observed among at least25% of low mass RGB stars and typical red amplitudes amp R donot exceed 0.8 magnitudes.In this section we apply methods of Sect. 4 to the time-filtered light curves of all EROS LMC and SMC red variablestars, whether known to display an LSP or not. In the processwe use the fact that our procedure does not require a known pe-riod. By employing the filters described in Sect. 3 we extractedseparate light curves for fast and slow variations. The cut-o ff fre-quency of our filters depends on the mean magnitude to ensure aproper split of B and D sequences in systems known to displayLSPs. Thus we obtain two di ff erent sets of amplitude and slope a V - l ong a V-short
LMC
0 0.2 0.4 0.6 0.8 1 a V - l ong a V-short
SMC
Fig. 16.
Correlation between the colour slope parameter of LSPsand the shorter period for EROS LMC and SMC data.parameters amp V − short and amp V − long , a V − short and a V − long fromrespectively high- and low-pass filtered light curves.In Fig. 15 we plot long-time amplitudes of variation of mag-nitude against short time ones, amp V − long v.s. amp V − short for allEROS LMC and SMC data. Stars marked in Fig. 14 as pos-sessing relatively large colour magnitude amp VI also exhibit absolutely large magnitudes amp V on at least one time scale.Although the amplitudes in Fig. 15 were estimated indepen-dently from two di ff erent light curves, they seem correlated. Aconsistent yet non-unique explanation would involve a similarmechanism for the short and long light variations.A stronger argument supporting the similarity of mecha-nisms of short and long time variations stems from the tight cor-relation of the short and long time scale slopes a short and a long re-vealed in Fig. 16. As discussed in Sect. 4 the two separate blobsin Fig. 16 correspond to C- and O- rich stars. The presence of justtwo such blobs rather than three or four at square vortices pro-vides striking demonstration that short and long time scale vari-ations both depend in the same way on surface chemical prop- ariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds 13 erties. Combined evidence from Figs. 15 and 16 indicates thatboth long and short time scale variations are due to the reactionof the stellar photosphere to similar kind of perturbations. Wecaution to not overinterpret this result. Firstly, our data containboth stars with and without known LSPs, and most light curvesexhibit both periodic and irregular variations. However, it mustbe remembered that LSP amplitudes are not that small, and theyare present in a sizable fraction of stars. If the LSP were pro-duced away from the photosphere, one could expect to see somesubstructure within both C and O blobs in Fig. 16, so apparentlack of any internal structure in these blobs is consistent withLSPs being caused by the same kind of photosphere response asfor the irregular variations and for the short period pulsations.In this context we stress that the EROS two-band observationsare strictly simultaneous; hence our conclusions on photosphereevolution involve no interpolation or implicit light curve models.
7. Conclusions.
A variable star during each cycle completes a closed loop on thecolour-magnitude diagram. Non-periodic variables travel moreinvolved routes. For each red variable star from the EROS sur-vey, we derived a width and average slope of these figures, re-spectively amp VI and a V . In doing so, we benefitted from re-liable colours obtained from EROS simultaneous two-band ob-servations. In this way our analysis is less a ff ected by variabilityand / or time sampling patterns. In particular, the gaps and alias-ing pose no big problem for us as long as the data cover most ofthe pulsation period. This is a much less demanding requirementthan a span of several cycles needed for reliable period analysis.The price paid in the process is a loss of any extra information;nevertheless, our analysis yields independent results that supple-ment more traditional period studies.Our key method derived in Sect. 4.1 relies on the parameters a V and amp VI derived from pure visual observations. For its test-ing and verification we cross-referenced stellar positions fromthe EROS, OGLE and MACHO optical surveys with the infrared2MASS catalogue. K magnitudes from the last catalogue weretreated as indicators of stellar mean luminosity. Such a proce-dure is reliable for a known distance because it has little K bandextinction and small bolometric correction for red variables. Tocompletely free our optical luminosities from extinction, we em-ployed the Wesenheit index. However, our key parameters result a V and amp VI are independent of distance and magnitude val-ues. The range and correlation of two band magnitude changesare the only parameters that are important for us.We demonstrated that in the a V and amp VI diagram, red vari-able stars form two well defined bands along a V = . .
65 lines. The bands occupied the same location for both theLMC and SMC stars. We argued that such a diagram consti-tutes a new method for di ff erentiating of C- and O-rich RGBstars from purely visual observations. So far, e ff ective photomet-ric methods have relied on infrared observations. In fact, the di-chotomy of C / O star distribution becomes even more prominentin the slope a V - K luminosity and slope- (J-K) colour diagramsfor all stars from our sample. The clustering is particularly pro-nounced, both for LMC and SMC, in the slope-luminosity dia-gram. There the AGB and RGB stars separate well, apart fromthe usual C / O split of a V . In this particular diagram stellar evo-lutionary tracks RGB-TRGB-AGB(O)-AGB(C) are particularlywell defined. While the detailed location of clusters in our di-agnostic diagrams does depend on passbands, it is clearly man-ifested both for both EROS and OGLE two-band photometries. However, the bands employed by MACHO are not suitable toour classification method.The final proof of the physical meaning of the clusteringobserved in our diagrams stems from the cross-check with cat-alogues of C-rich stars. The overwhelming majority of C-richstars from catalogues by Kontizas et al. (2001), Groenewegen(2004), Rebeirot et al. (1993), Morgan & Hatzidimitriou (1995),for LMC and SMC, belongs to the low- a V slope cluster. Thusit appears that indeed the C- and O-rich stars belong to separateclusters in our a V vs. amp VI diagnostic diagram. In this way wediscovered and verified a new method of distinguishing betweenC- and O-rich stars. Our method works for sparse coverage intwo-colour light curves in the bands resembling V and I . Sincewe rely on colours, the measurements in both filters should be(nearly) simultaneous. Our method was tested successfully forEROS-2 LMC and SMC observations and also for OGLE data.It does not seem to su ff er from any metallicity e ff ect as clus-ter locations for the LMC and SMC were identical. Using sim-ple simulations based on realistic evolutionary models of RGB,we demonstrated plausible cause of the e ff ect revealed by ourmethod; however, for as broad filters as those used by MACHOour method fails. One future application of our diagrams is totest the pulsation evolutionary models on a large population ofRGB and AGB stars.Using our method of di ff erentiating the O- and C-rich starswe were able to derive the population C / O star ratio, an indica-tor of the mean metallicity of a stellar population, as well as atracer of the history of stellar formation (Cioni et al. 2006). Ourselection can recognise more C-rich stars than using J − K > . / O ratio. Thus we wereable to produce C / O maps for the LMC and SMC.We payed some attention to colour correlation properties ofthe LSP compared to the short primary pulsation (SPP). Our re-sults provide some evidence favouring origin of both LSP andSPP in the stellar photosphere. This follows from the correla-tion of colour-magnitude slopes and separately from correlationof amplitudes for the LSP and SPP. In other words, both SPPand LSP depend on the chemical (C / O) properties of the pho-tosphere. The colour variations would be consistent with mod-ulation of the e ff ective temperature. This seems to exclude anyaspect e ff ects, e.g. eclipses, as a cause of LSP; however, usingour purely photometric observations it would be premature toconclude that both SPP and LSP clocks are due to pulsation.However, both clocks should somehow a ff ect the photosphere insimilar ways. Acknowledgements.
We would like to thank Jim Rich for his careful readingof the manuscript and the anonymous referee for helpful comments. This workmade use of EROS-2 data, which were kindly provided by the EROS collab-oration. The EROS (Exp´erience de Recherche d’Objets Sombres) project wasfunded by the CEA and the IN2P3 and INSU CNRS institutes. We acknowl-edge use of data the Two Micron All Sky Survey, which is a joint projectof the University of Massachusetts and the Infrared Processing and AnalysisCenter / California Institute of Technology, funded by the National Aeronauticsand Space Administration and the National Science Foundation. This work wascarried out, for ASC, JPB, JBM, and MW, within the framework of the EuropeanAssociated Laboratory “Astrophysics Poland-France”. ASC acknowledges sup-port by the Polish grant MNiSW N N203 3020 35.
References
Afonso, C., Albert, J. N., Alard, C., et al. 2003, A&A, 404, 145Alard, C., Blommaert, J. A. D. L., Cesarsky, C., et al. 2001, ApJ, 552, 289Alcock, C., Allsman, R., Alves, D., et al. 2003, VizieR Online Data Catalog,2247, 0Alcock, C., Allsman, R. A., Alves, D., et al. 1997, ApJ, 486, 697Ansari, R. 1996, Vistas in Astronomy, 40, 519
Aubourg, E., Bareyre, P., Brehin, S., et al. 1995, A&A, 301, 1Bergeat, J., Knapik, A., & Rutily, B. 2001, A&A, 369, 178Bond, I. A., Abe, F., Dodd, R. J., et al. 2001, MNRAS, 327, 868Bowen, G. H. & Willson, L. A. 1991, ApJ, 375, L53Bressan, A., Chiosi, C., & Tantalo, R. 1996, A&A, 311, 425Bruzual, G. & Charlot, S. 2003, MNRAS, 344, 1000Cioni, M.-R., Loup, C., Habing, H. J., et al. 2000a, A&AS, 144, 235Cioni, M.-R. L., Blommaert, J. A. D. L., Groenewegen, M. A. T., et al. 2003,A&A, 406, 51Cioni, M.-R. L., Girardi, L., Marigo, P., & Habing, H. J. 2006, A&A, 448, 77Cioni, M.-R. L. & Habing, H. J. 2003, A&A, 402, 133Cioni, M.-R. L., Habing, H. J., & Israel, F. P. 2000b, A&A, 358, L9Cioni, M.-R. L., Marquette, J.-B., Loup, C., et al. 2001, A&A, 377, 945Cioni, M.-R. L., van der Marel, R. P., Loup, C., & Habing, H. J. 2000c, A&A,359, 601Costa, E. & Frogel, J. A. 1996, AJ, 112, 2607Derekas, A., Kiss, L. L., Bedding, T. R., et al. 2006, ApJ, 650, L55Derue, F., Marquette, J.-B., Lupone, S., et al. 2002, A&A, 389, 149Feast, M. W., Glass, I. S., Whitelock, P. A., & Catchpole, R. M. 1989, MNRAS,241, 375Fisz, M. 1963, Probability Theory and Mathematical Statistics (New York:Wiley)Fraser, O. J., Hawley, S. L., Cook, K. H., & Keller, S. C. 2005, AJ, 129, 768Frogel, J. A., Mould, J., & Blanco, V. M. 1990, ApJ, 352, 96Girardi, L. & Marigo, P. 2007, in Astronomical Society of the Pacific ConferenceSeries, Vol. 378, Why Galaxies Care About AGB Stars: Their Importance asActors and Probes, ed. F. Kerschbaum, C. Charbonnel, & R. F. Wing, 20–24Groenewegen, M. A. T. 2004, A&A, 425, 595Groenewegen, M. A. T. & de Jong, T. 1993, A&A, 267, 410Hoefner, S., Fleischer, A. J., Gauger, A., et al. 1996, A&A, 314, 204Iben, Jr., I. 1981, ApJ, 246, 278Iben, Jr., I. & Renzini, A. 1983, ARA&A, 21, 271Ireland, M. J., Scholz, M., Tuthill, P. G., & Wood, P. R. 2004a, MNRAS, 355,444Ireland, M. J., Scholz, M., & Wood, P. R. 2004b, MNRAS, 352, 318Ita, Y., Tanab´e, T., Matsunaga, N., et al. 2004a, MNRAS, 353, 705Ita, Y., Tanab´e, T., Matsunaga, N., et al. 2004b, MNRAS, 347, 720Izzard, R. G., Tout, C. A., Karakas, A. I., & Pols, O. R. 2004, MNRAS, 350, 407Kiss, L. L. & Bedding, T. R. 2003, MNRAS, 343, L79Kiss, L. L. & Bedding, T. R. 2004, MNRAS, 347, L83Kontizas, E., Dapergolas, A., Morgan, D. H., & Kontizas, M. 2001, A&A, 369,932Lanc¸on, A. & Mouhcine, M. 2002, A&A, 393, 167Lasserre, T., Afonso, C., Albert, J. N., et al. 2000, A&A, 355, L39Lebzelter, T. & Hinkle, K. H. 2002, A&A, 393, 563Lebzelter, T. & Wood, P. R. 2005, A&A, 441, 1117Maraston, C. 1998, MNRAS, 300, 872Maraston, C. 2005, MNRAS, 362, 799Marigo, P., Girardi, L., & Bressan, A. 1999, A&A, 344, 123Marigo, P., Girardi, L., Bressan, A., et al. 2008, A&A, 482, 883Marigo, P., Girardi, L., & Chiosi, C. 2003, A&A, 403, 225Matsunaga, N., Fukushi, H., & Nakada, Y. 2005, MNRAS, 364, 117Morgan, D. H. & Hatzidimitriou, D. 1995, A&AS, 113, 539Mouhcine, M. 2002, A&A, 394, 125Mouhcine, M. & Lanc¸on, A. 2002, A&A, 393, 149Mouhcine, M. & Lanc¸on, A. 2003, MNRAS, 338, 572Nicholls, C. P., Wood, P. R., Cioni, M., & Soszy´nski, I. 2009, MNRAS, 399,2063Noda, S., Takeuti, M., Abe, F., et al. 2002, MNRAS, 330, 137Noda, S., Takeuti, M., Abe, F., et al. 2004, MNRAS, 348, 1120Olivier, E. A. & Wood, P. R. 2005, MNRAS, 362, 1396Paczynski, B., Stanek, K. Z., Udalski, A., et al. 1994, ArXiv Astrophysics e-print: astro-ph //